Welsh Accent has nothing to do with it- I have a friend in Caernarfon, who is "Rel Cofi" in Welsh- but in English sounds very erm...well off Kensington
Well, that is where she learned to speak it , having had to live with relations from age 5 to 11....then back to home and school in C'nafron
It depends where you are in Cardiff as well, what shops/pubs/clubs you go to-who you work for too.
It isn't always easy to get shops to allow their employees to have the pin badge that would denote Welsh Speaker/Learner either

A lot of people wont speak Welsh on the street, or in shops- even to people they KNOW are Welsh speakers too

When my cat went missing in the summer, I walked round the whole block (40 or so houses) asking them to check their garden sheds. Not a single person I spoke to was Welsh. A few eastern European migrants, a few Asian families but mostly English speakers with English accents (not even Cardiff accents!).

(By the way, to clarify, I'm talking about Welsh as the first language, rather than English-but-born-in-Wales).

In my experience, urban areas lose their Welsh heritage, whilst rural communities maintain it. Personally, I think that's linked to how people voted in the devolution referendum. I know most people where I grew up were furious that the NAW was homed in Cardiff, which voted against devolution!

Now we've got onto language. Do many English immigrants actually try to learn Welsh, and how do they do it?

I'm rubbish at languages, but think I ought to give it a try, even if it's just so I can pronounce place names!

Plenty of evening classes run by local authorities. The Urdd also used to run them at their centres and they were generally better.
Many areas will have a free Welsh local news thing. Lots of this info will be in your local library.

Then practise- listen to Radio Cymru, have it on as audio wallpaper to get yours ears used to the flow before you try and 'change gear' linguistically.
You will probably be able to find a group of learners who socialize once a week, then you will find what shops/pubs are the ones to find Welsh speakers in.

This applies to whatever country/language I should imagine.

A family moved to Cardiff about eight years ago, and they had two children in Ysgol Gyfun Glantaf (one of the local Welsh Medium Secondary Schools, one in Emyr's year, one in Osian's.
They were all perfectly bilingual....Welsh and Spanish

Certainly-things are done differently wherever you go, one learns and adapts, not expecting. things to be done your way by everyone.
On the other hand you don't have to give up your own way of doing things either.

Now we've got onto language. Do many English immigrants actually try to learn Welsh, and how do they do it?

I'm rubbish at languages, but think I ought to give it a try, even if it's just so I can pronounce place names!

We're in another, "fusion", country...the Welsh Marches. Our farm is in Wales yet we look west into England as in some of the fields are split in half and the local pub and its car park are in separate countries. The maternity unit is in England so many Welsh children are identity confused I expect. My children learn Welsh in a Welsh primary school and are then catchmented for an English high school. And the place names around here are corrupted from Welsh.

So, no, we don't learn Welsh...although my eldest two at a Welsh university in a more Welsh area are picking it up as it's more widely spoken.

It felt like emigrating going to Lincolnshire for me didn't like it in the slightest *scowl* I only moved there on the proviso we left...pronto! It never happened, so I've made good my escape Feel much more at home in Yorkshire. Despite their six fingers and other inferiorities, I feel a kinship with them as I did grow up very close to the border.

BMS, one of those in Cardiff with a Welsh accent was probably my sister, who is as English as they come, but "learned" a Cardiff accent as soon as she moved there aged 18. 30 years on, it's well-set-in now

Nat, I hated Lincs, too. Lived there for 3 and a half years, and spent most of that time counting down to moving away!!

Eldest son went to Cardiff Uni, and has a Welsh girlfriend,also works for the Welsh Goverment.Have to say that after 8 years he sounds more Welsh than English.
He,s gone back to his roots though, as our surname is Evans, and OH,s grandad was a gamekeeper in Crickhowell.